Pre-Algebra Examples

$\frac{5}{2 x + 1} + \frac{8}{4 x + 2}$

Step 1

Cancel the common factor of $8$ and $4 x + 2$ .

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Step 1.1

Factor $2$ out of $8$ .

$\frac{5}{2 x + 1} + \frac{2 \cdot 4}{4 x + 2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4 x$ .

$\frac{5}{2 x + 1} + \frac{2 \cdot 4}{2 (2 x) + 2}$

Step 1.2.2

Factor $2$ out of $2$ .

$\frac{5}{2 x + 1} + \frac{2 \cdot 4}{2 (2 x) + 2 (1)}$

Step 1.2.3

Factor $2$ out of $2 (2 x) + 2 (1)$ .

$\frac{5}{2 x + 1} + \frac{2 \cdot 4}{2 (2 x + 1)}$

Step 1.2.4

Cancel the common factor.

$\frac{5}{2 x + 1} + \frac{2 \cdot 4}{2 (2 x + 1)}$

Step 1.2.5

Rewrite the expression.

$\frac{5}{2 x + 1} + \frac{4}{2 x + 1}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 + 4}{2 x + 1}$

Step 3

Add $5$ and $4$ .

$\frac{9}{2 x + 1}$